SOLUTION: (7) Question: Solve for y: -2y-2=sqrt2y^2-7-7. You many include extraneous solutions. (a) 2, 8 (b) -2,8 (c) -2, -8 (d) 2, -8 Please be specific as to which letter answer

Question 30475: (7) Question:
Solve for y: -2y-2=sqrt2y^2-7-7. You many include extraneous solutions.
(a) 2, 8
(b) -2,8
(c) -2, -8
(d) 2, -8
Please be specific as to which letter answer is correct. Thanks!
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
If the given problem is
-2y-2 =sqrt(2y^2-7)-7 ----(1)
-2y-2+7 = sqrt(2y^2-7)
-2y+5 = sqrt(2y^2-7)
Squaring both the sides
(5-2y)^2 = (2y^2-7)
[by additive commutativity -2y+5 = 5-2y and using [sqrt(p)]^2 = p ]
25+4y^2-20y = 2y^2-7 (using (a-b)^2 = a^2+b^2-2ab and here a = 5 and b = 2y )
(4y^2-2y^2)-20y+25+7 = 0 (grouping like terms,changing sign while changing side)
2y^2-20y+32 = 0
dividing by 2
y^2-10y+16 =0
y^2-8y-2y+16 = 0
(since sum is -10 and product is 16, the two terms into which the middle term is split are -8y and -2y so that -10y = (-8y)+(-2y)
and (-8y)X(-2y) = 16y^2 = (y^2)X(16) )
y(y-8)-2(y-8) = 0
yp-2p = 0 where p= (y-8)
p(y-2) =0
(y-8)(y-2) = 0
(y-8) = 0 gives y = 8
and (y-2) = 0 gives y = 2
Answer: y = 2 and y = 8
which is your choice (a) 2,8

RELATED QUESTIONS
Question: Solve for y:-2y-2= sqrt2y^2-7-7 (You may include extraneous solutions.)... (answered by ikdeep)

(7) Question: Solve for y: -2y-2 = sqrt 2y^2-7 -7 (You may include extraneous solutions) (answered by sdmmadam@yahoo.com)

(7) Question: How many solutions for x are there in this equation: sqrt x-4 - sqrt x+8... (answered by josmiceli)

Solve: (2/5)^7-x =5/2 A. 6 B. 7 C. 8 D.... (answered by Fombitz)

(8) Question: Choose the nonlinear systesm below that have (x,y)=(4,3) as on of their... (answered by venugopalramana)

Question: How many solutions for x are there is the equation: sqrtx-4 -sqrtX+8 =2?... (answered by ikdeep)

(2^10 �2^9)(2^8 � 2^7) = a)2^2 b) 2^4 c) 2^8 d) 2^16 (answered by checkley77)

Solve y=-x+8 and x+y=7 A) This system has no solutions. B) This system has infinitely... (answered by stanbon,ewatrrr)

7/8 -... (answered by checkley77)